I can not comment on 1 but 2-4 are correct.
But at least in Germany the term airport of entry is maybe not specific enough. There are airports with customs, others with passport control and some with both.
If you want to fly that far for example my home base EDAZ south of Berlin offers both. 2h prior notice for customs, passport control is possible at any time without prior notice. Reasonable fees, AVGAS approximately 2,55 EUR.
What confuses me is if you look at Jeppesen' s airport data on Jepp FD for say EDAZ it is not described as an Airport of Entry but clearly as you say it is capable of offering all the services of an Airport of Entry.
Some of the larger airports in Germany are described as Airports of Entry others just list "Customs". If Customs are listed surely its an Airport of Entry by definition so why not list it as such.
EDAZ would be good for me. Thanks
I´d suggest to forget about the Airport of Entry term for this case, just look for an airfield where customs are offered and give them a call to confirm(for sure!). An excellent airport for this used to be Straubing (EDMS), but it´s a bit south of your way - no prior notice required, just fill a simple form after arrival. They´ll fax to police and ask you to wait 10-15 minutes to give them a chance to see you. They showed up only once in my several landings and later I discovered the officer was just keen on seeing a small aircraft Schönhagen (EDAZ) used to be good as well, but still probably too south for you.
In the standard international aviation products such as Jepps, and databases such as this and this, the word "Customs" is traditionally used to mean that you can fly there from another country.
The more subtle concepts e.g. passport controls versus customs (goods and vehicles) controls and peculiar European stuff like Schengen, are disregarded. Especially as Switzerland, Norway, and Greece disregard Schengen for all practical purposes.
It probably all goes back to the bizjet world, which is where most of the world's aviation revolves, and where nobody has the time to mess about. Your boss says his wife wants to do a spot of shopping in Kazachstan, tomorrow morning please. You plan the flight, phone the handling agent there, file the flight plan, and fly there...
Unfortunately, in stuff like the AIPs, things get confusing at times. But "real pilots" never read the AIPs (which are published to discharge the national obligations to ICAO and were never intended for a pilot to actually fly with). Real pilots pay Jepps $10k/year to present them with nice clear consistent stuff they can fly with.
The above is only slightly tongue in cheek 
Speaking of fuel prices, they are universally lower in Belgium than in Germany and the Netherlands. My personal favourite is Liège EBLG - a full-fledged international airport (albeit mostly a cargo one) with a landing fee of €14.
